Material‐dependent crack‐tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials

Wang Yongxiang; Waisman Haim

摘要

Summary xml:id="nme5566-para-0001">A novel set of enrichment functions within the framework of the extended finite element method is proposed for linear elastic fracture analysis of interface cracks in bimaterials. The motivation for the new enrichment set stems from the revelation that the accuracy and conditioning of the widely accepted 12‐fold bimaterial enrichment functions significantly deteriorates with the increase in material mismatch. To this end, we propose an 8‐fold material‐dependent enrichment set, derived from the analytical asymptotic displacement field, that well captures the near‐tip oscillating singular fields of interface cracks, including the transition to weak discontinuities of bimaterials. xml:id="nme5566-para-0002">The performance of the proposed material‐dependent enrichment functions is studied on 2 benchmark examples. Comparisons are made with the 12‐fold bimaterial enrichment as well as the classical 4‐fold homogeneous branch functions, which have also been used for bimaterials. The numerical studies clearly demonstrate the superiority of the new enrichment functions, which yield the most accurate results but with less number of degrees of freedom and significantly improved conditioning than the 12‐fold functions. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：id =“nme5566-abs-abs-0001”> <标题类型=“main”>摘要</ title> < P XML：ID =“NME5566-PARA-0001”>提出了延伸有限元方法框架内的新型富集功能，用于双材料界面裂缝的线性弹性断裂分析。新的浓缩集中的动机源于启示的启示，即广泛接受的12倍的双材料富集功能的准确性和调理随着材料不匹配的增加而显着恶化。为此，我们提出了一种从分析渐近位移场的8倍的材料依赖性富集集合，该集体井井地捕获界面裂缝的近尖振荡奇异场，包括过渡到双肢物的弱不连续性。</ p > XML：ID =“NME5566-PARA-0002”>在2个基准示例中研究了所提出的材料依赖性富集功能的性能。使用12倍的双层富集以及经典的4倍均匀分支功能进行比较，这也已用于双材料。数值研究清楚地展示了新的富集功能的优越性，从而产生了最准确的结果，但具有较少数量的自由度和比12倍函数显着改善调节。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20801/'>《International Journal for Numerical Methods in Engineering》</a> <b style="margin: 0 2px;">|</b><span>2017年第11期</span><b style="margin: 0 2px;">|</b><span>共24页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wang Yongxiang&option=202" target="_blank" rel="nofollow">Wang Yongxiang;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Waisman Haim&option=202" target="_blank" rel="nofollow">Waisman Haim;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Civil Engineering &</p> <p>Engineering MechanicsColumbia UniversityNew York 10027 NY USA;</p> <p>Department of Civil Engineering &</p> <p>Engineering MechanicsColumbia UniversityNew York 10027 NY USA;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/6940.html" title="工程数学">工程数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=bimaterials&option=203" rel="nofollow">bimaterials;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=crack‐tip enrichment functions&option=203" rel="nofollow">crack‐tip enrichment functions;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=extended finite element method&option=203" rel="nofollow">extended finite element method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=interface crack&option=203" rel="nofollow">interface crack;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=oscillatory singularity&option=203" rel="nofollow">oscillatory singularity;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=weak and strong discontinuities&option=203" rel="nofollow">weak and strong discontinuities;</a> </p> <div class="translation"> 机译：双材料;裂缝尖端富集功能;延长有限元法;界面裂缝;振荡奇点;弱和强度不连续; 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